Carry On Cowboy

A Town Called Mercy will mark the Doctor's first televised return to the Wild West of the United States since 1966's The Gunfighters. In that story, the first Doctor and companions Steven and Dodo landed in the town of Tombstone, Arizona, in October 1881. The Doctor is initially mistaken for the notorious Doc Holliday. The travellers get caught up in the infamous gunfight at the OK Corral.

If you thought that this was the programme's only brush with the Western genre then you'd be wrong. It's just that the other stories transplanted the Western into outer space.
Robert Holmes' The Space Pirates is pure Western but without the horses. The Wild West is the outer frontiers of space. The Pirates are gold-mining claim jumpers. Milo Clancey is an old '49er. His costume and accent / language reflect this. General Hermack and his Space Corp are the 7th Cavalry, trying to impose order in this lawless region.

Then there is Holmes' other story - The Power of Kroll. This could represent any kind of colonialism, but I think - knowing his love of the Western genre - that the "Swampies" are analogous to Native Americans. We're in another wild frontier land and this time the gold miners want to remove the native peoples from their land - and one of them is willing to sell arms to start a war the natives can't hope to win. There are several Hollywood Westerns in which a dodgy gun runner tries to sell guns to the Indians.

If you accept that Kroll has Western origins, then you would also have to see The Caves of Androzani in the same light - as Holmes borrowed quite a few elements from his earlier story.
One last Western reference staring everyone in the face but always overlooked is the eighth Doctor's costume - for a costume it is. He "borrowed" it from a hospital locker - someone's Millennium Eve fancy dress outfit. Remember he discarded a gun and holster - it is the costume for a  gentleman gunslinger of the Old Wild West, possibly even Doc Holliday himself.